l(U) A=a, Z=z, X=x=0   (a,z,x) A ZX       l(u) = 0 a.s.


Following similar reasoning as in Section , we can estimate the bridge function \(\hat{h}: \mathcal {A} \times \mathcal {X} \times \mathcal {W} \rightarrow \mathbb {R}\)  by minimizing the following loss:

h = h Hh L(h),    L(h) = [Y,A,Z, X](Y - [W|Z,A,X]h(A,X,W))2 + (h).

Given bridge function, we can estimate the structural function by

fstruct(a) = [X,W]h*(a, X, W).

Similar to Mastouri and Zhu et al. [1]},
we model

[W|a,z]W(w) = V(A(1)(A) Z(Z)) X(1)(X))
